Elliptic curve isogeny class 25.1-f over number field \(\Q(\sqrt{5}, \sqrt{7})\)

• Base field: \(\Q(\sqrt{5}, \sqrt{7})\)
• Label: 4.4.19600.1-25.1-f
• Conductor: 25.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{5}, \sqrt{7})\)

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 15 x^{2} + 16 x + 29 \); class number \(1\).

Elliptic curves in class 25.1-f over \(\Q(\sqrt{5}, \sqrt{7})\)

Isogeny class 25.1-f contains only one elliptic curve.

Curve label	Weierstrass Coefficients
25.1-f1	\( \bigl[0\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} + \frac{13}{23} a + \frac{103}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{27}{23} a + \frac{106}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} + \frac{36}{23} a - \frac{81}{23}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph